 Solution

In uniform fields, a rigid neutral electric dipole with both charges moving at the selected common velocity has zero net translational force. To leading nonrelativistic order its torque is $\mathbf{\tau }=\mathbf{p}\times (\mathbf{E}+\mathbf{v}\times \mathbf{B})$, which also vanishes at the velocity-selector condition. Thus it continues undeflected and, initially nonrotating, does not start rotating in the ideal balanced fields. An unbalanced effective field could exert a torque; the dipole orientation is not otherwise specified.